“here is a room for you to live.”对还是“here is a room for you to live in.”呢？为什么？

“here is a room for you to live.”对还是“here is a room for you to live in.”呢？
here is a room for you to live in
因为动词live在这里不及物
live in the room是正确的用法这里介词不能省略

二楼说得很对,这种时候就应该把句式改成最简单的陈述句来看

第二个问题,因为where中包含了in在里面，这个类似于病宾语从句，如果不用where而用which的话就是which room do you live in?

here is a room for you to live in.
这里有一间房间让你住。
应给是live in a room.不能是live a room.live是不及物动词，要用介词。

to live in 是不定式做（room的）定语。所以是live in a room，live为不及物动词。eg：
he said he had nothing to worry about
there is a old man (for you)to look after
希望对你有所帮助

把这个句子语序倒一下你就知道了，You live in a room 而不是you live a room